Math 224 – Elementary Statistics



Statistics – Lab #5

Statistical Concepts

← Probability

← Binomial Probability Distribution

Calculating Binomial Probabilities

➢ Open a new MINITAB worksheet.

➢ We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name. Now enter the numbers zero through ten to represent all possibilities for the number of successes. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter the Number of trials: and Probability of success:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet.

➢ Now we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column.

➢ Finally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. Print the worksheet.

Plotting the Binomial Probabilities

➢ Create Bar Charts for the three binomial distributions above. Select Graph > Bar Chart and then for Bars represent: select values from a table and select OK. For graph 1 set Graph variables: equal to ‘one fourth’ and Categorical variable: to ‘success’, for graph 2 set Graph variables: equal to ‘one half’ and Categorical variable: to ‘success’, and for graph 3 set Graph variables: equal to ‘three fourths’ and Categorical variable: to ‘success’. Title (put your name in as the title) and print the graphs.

Calculating Descriptive Statistics

➢ Open the class survey results that were entered into the MINITAB worksheet.

➢ Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window. Again, print this information.

Short Answer Writing Assignment

If applicable, answers should be in complete sentences. Include copies of all print outs with this assignment.

1. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not necessary)

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2. Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary)

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3. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½.

4. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¼ and compare to the results from question 3.

5. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¾ and compare to the results from question 3.

6. Explain why the coin variable represents a binomial distribution and how it relates to the probabilities calculated in MINITAB when the probability of a success was ½.

7. Give the mean and standard deviation for the coin variable and compare these to the mean and standard deviation for the binomial distribution that was calculated in question 3. Explain how they are related.

8. For the following, identify the shape of the binomial distribution and explain why each shape occurred.

a. When the probability of a success was ¼?

b. When the probability of a success was ½?

c. When the probability of a success was ¾?

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